发表机构
University of Maryland, College Park; Northeastern University（马里兰大学帕克分校; 东北大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对周期格型图上的极大硬核模型，提出通用框架，验证其高、低活性下的结晶性，推导活性值估计以界定相共存区域，完善了Pirogov-Sinai理论在该类模型中的应用。
AI 中文摘要
我们研究周期格型图上的通用极大硬核模型。对于标准模型，高活性下可能出现相共存；而对于极大模型，该行为也可在足够低的活性值下发生。基于体积分配概念，我们提出一组统一假设，这些假设蕴含Peierls条件、配分函数的收敛团簇展开，进而为该类模型得到Pirogov-Sinai理论的结论。我们还针对多个示例（包括标准格型周期图）验证了这些假设，证明了高活性与低活性下的结晶现象。此外，我们推导了活性值的估计，以界定相图中的相共存区域，为此重写了Pirogov-Sinai理论推导中一个技术结果的证明。
英文摘要
We study general maximal hard-core models on periodic lattice-type graphs. While for standard models, phase coexistence may arise for high activity, for maximal models this behavior may occur also for sufficiently low activity values. Relying on the concept of volume allocation, we develop a {\em unified set of assumptions} that imply the Peierls condition, a convergent cluster expansion for the partition function, and hence the conclusions of Pirogov-Sinai theory for this class of models. We further check these assumptions for a number of examples including standard lattice-type periodic graphs, proving crystallization for both high and low activity. We also derive estimates for the values of activity that bound the phase coexistence regions in the phase diagram, rewriting for this purpose the proof of a technical result in the derivation of Pirogov-Sinai theory.
Comments33pages, 11 figures
